Lucinda Williams is late. As the DJ puts on another record, the sound of a slow hand-clap begins. Finally, the lights dim and Williams strolls on. "You're late. It better be good!" shouts a voice in the darkness. Williams is not fazed: "It will be fuckin' good!"

With her jeans tight enough to threaten her blood vessels and a shock of yellow hair that could have fallen on her head in a storm, Williams is the epitome of the rock outlaw. Dubbed "the female Keith Richards", which somehow insults them both, and "America's greatest songwriter", which may be about right, Williams has won Grammys but is a world away from the artists who usually win mainstream honours.

You could believe she was late because she hitched a ride in a truck after holding up a bank, while her voice is twice as loud as the band, who won't be complaining. Perhaps if her songs weren't as heralded, people would realise that Williams is one of the most gifted vocalists of our time.

The slurred, perfectly sleepy vocal cracks tantalisingly as it tumbles from her mouth. In the particularly sublime Ventura, she goes from eulogising the ocean to throwing up over the toilet bowl within a couple of lines.

"People magazine said: 'Lil Kim she's not'," she snipes, after a spoken, almost rapped section. The expression is accusatory. "Yeaaaah?!" But behind the stance she's vulnerable, self-deprecating and funny, making up the set as she goes along. "I'll throw in a couple of extra songs to make up for them stinkers."

Williams hasn't toured here for 15 years, so mixes her fantastic new World Without Tears album with a clutch of older songs. Playing theatres has meant an unfamiliar atmosphere - "Ahhh'm used to playin 'rowdy bars" - but the trade-off is an exquisite sound that adds to the power of songs as diverse as Real Live Bleeding Fingers and Broken Guitar Strings ("Dirty words, hero-inn!") and Essence ("Kiss me hard, make me wonder who's in charge").

She encores with Drunken Angel (dedicated to Kurt Cobain and "so many more") and Sweet Old World, songs that refer to a supernatural world, which, on this form, Williams could easily have come from.

· At Shepherd's Bush Empire, London W12 (0870 771 2000), tonight.